Gravity-driven demixing experiments of mechanically mixed binary-liquid mixture are performed at various temperatures. A steady state is observed in which the demixing rate is nearly constant. We find that the droplet size in the demixing zone grows only for a short time. During most of the demixing process, the size of these droplets is stabilized by the flow itself. A relationship between the characteristic demixing time-tau and the reduced temperature-epsilon is found, i.e. tau approximately epsilon(-theta) with theta = 0. 54 +/- 0.03. A phenomenological model in which the demixing process is considered as a flow through a porous medium is proposed to explain the experimental results.